Singular Value Decomposition

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Related lectures (44)

Linear Systems: Diagonal and Triangular Matrices, LU Factorization Log in to Mediaspace to watch this video

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Matrix Diagonalization: Spectral Theorem Log in to Mediaspace to watch this video

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Singular Value Decomposition Log in to Mediaspace to watch this video

Covers the Singular Value Decomposition (SVD) of a matrix and its applications.

Diagonalization of Symmetric Matrices Log in to Mediaspace to watch this video

Explores the diagonalization of symmetric matrices through orthogonal decomposition and the spectral theorem.

Orthogonal Projection Theorems Log in to Mediaspace to watch this video

Covers the theorems related to orthogonal projection and orthonormal bases.

Orthogonality and Subspace Relations Log in to Mediaspace to watch this video

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Orthogonal Projection: Spectral Decomposition Log in to Mediaspace to watch this video

Covers orthogonal projection, spectral decomposition, Gram-Schmidt process, and matrix factorization.

Linear applications and eigenvalues Log in to Mediaspace to watch this video

Covers the representation of linear applications through matrices, diagonalizable matrices, bases, dot product, orthogonality, and orthogonal vectors.

Determinants: Special Linear Groups and Matrix Properties Log in to Mediaspace to watch this video

Explores the special linear group, matrix properties, and determinant theorems.

Eigenvalues and Eigenvectors: Real Solutions Log in to Mediaspace to watch this video

Explains eigenvalues and eigenvectors, focusing on real solutions and their properties.

Linear Transformations and Change of Bases Log in to Mediaspace to watch this video

Covers linear transformations, change of bases, and diagonalization of matrices.

Vector Spaces and Bases Log in to Mediaspace to watch this video

Explores vector spaces, linear independence, and bases, illustrating their importance through examples in R2 and R3.

Spectral Clustering: Finding Clusters Log in to Mediaspace to watch this video

Explores Spectral Clustering, eigenvalue decomposition, Laplacian matrices, and cluster identification through eigenvector projections.

Reciprocal Space and Bragg Condition Log in to Mediaspace to watch this video

Explores complex numbers in reciprocal space and the Bragg condition, emphasizing linear algebra's importance for engineers.

PCA and BBP Phase Transition Log in to Mediaspace to watch this video

Covers PCA application and BBP phase transition in a card game dataset.

Gauss-Jordan Method Log in to Mediaspace to watch this video

Introduces the Gauss-Jordan method for solving linear equations and explores unique solutions and efficiency comparisons.

Untitled Log in to Mediaspace to watch this video

Linear Applications and Simple Objects Log in to Mediaspace to watch this video

Covers the bijection between linear applications from L(X) to V and applications from X to U(V).

Matrix Multiplication: Associativity Property Log in to Mediaspace to watch this video

Explores the associativity property of matrix multiplication for proving products equal to zero.

Linear Systems: Resolution and Solutions Log in to Mediaspace to watch this video

Explores the resolution of linear systems and the distinction between homogeneous and non-homogeneous equations.

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